6) \( 3 x+2 y>4 \)

To solve \( 3x + 2y > 4 \), let's first rewrite it as an equation \( 3x + 2y = 4 \) to find the boundary line. When you graph this line on a coordinate plane, you'll see that it separates the plane into two half-planes. You'll shade above the line for the inequality \( 3x + 2y > 4 \) since we are looking for values where the left side is greater than 4. Now, a fun tip: Choose a test point that's not on the line (like (0,0)) to determine which side to shade. Substituting (0,0) into the inequality gives \( 0 > 4 \), which is false, so you shade the opposite side. Voila, you've got your solution region!